Introduction to Binary Octal and Hexadecimal Numbers Part

Introduction to Binary, Octal and Hexadecimal Numbers Part 1 – General Notation Thaddeus Konar Slide # 1 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Decimal Integers 89340987983472987632 There is nothing ‘unique’ about number 10, but because we have 10 fingers, the decimal notation (from 09832198798237986498762380236409 Latin decem and Greek Deka: 10) seems ‘natural’ to us. If the world would be like Simpsons (and I am glad it is not) the natural notation would be octal (8 fingers) 4576 8374567301 Slide # 2 9654327 78543 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Decimal Integers Each digit (counting from the right) represents next power of ten, the rightmost digit represents 1 s, next digit represents 10 s, next 100 s, and so on: …, 10000, 100, 1 which is the same as: …, 104 , 103, 102, 101, 100 (Please remember that any number X to zero (0) power equals 1!) X 0 = 1 Slide # 3 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Decimal Integers (cont) 7845 means: (5*1)+(4*10)+(8*100)+(7*1000) and this is same as: (5*100)+(4*101)+(8*102)+(7*103) Slide # 4 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Decimal Integers (Cont) What does 58345 ‘really’ mean: 58345 5*1 4 * 10 3 * 100 8 * 1000 5 * 10000 Slide # 5 =5 =40 =300 =8000 =50000 =58345 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

Decimal Integers (cont) Lets look at the properties of the decimal integers: Base = 10 (1, 100, …) (100, 101 , 102 , …) Digits range: 0 -> 9 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Number of possible values represented by single digit: 10 Please note that number of digits equals Base, and range goes from zero to (Base – 1). Digits range: 0 -> (Base - 1) Number of possible values represented by single digit: Base Slide # 6 Binary, Octal and Hex Numbers Copyright Thaddeus Konar

General Notation Any number is represented by combination of single digits Dx, where x is the position of the digit counting from the right. The value of Dx can be only the digits between (and including) 0 and (Base-1). …D 5 D 4 D 3 D 2 D 1 D 0 Using our example decimal number 7845 D 0 =5, Slide # 7 D 1=4, D 2=8, Binary, Octal and Hex Numbers Copyright Thaddeus Konar and D 3 =7

General Notation (cont) We can see that any number really means: (D 0*B 0)+(D 1*B 1)+(D 2*B 2)+(D 3*B 3)+…(Dn*Bn) In our example number 7845 (base 10) means: (5*100)+(4*101)+(8*102)+(7*103)=5+40+800+7000 Slide # 8 Binary, Octal and Hex Numbers Copyright Thaddeus Konar